Learning the function concept by exploring digital images as functions

Abstract

Despite the function concept being fundamental to mathematics, an adequate understanding of this concept is often lacking. This problem is prevalent at all levels of education and is reported in many countries. This article reports on a new pedagogical strategy based on exploring photographs or digital images as functions. The objective of this study was to determine if the Image Functions Intervention (IFI) could be considered sound and viable with respect to the learning of the function concept. A two-part approach was used. The first part used the Action-Process-Object-Schema (APOS) theory as a theoretical framework for evaluating the IFI. The second part implemented the IFI with a group (n = 27) of undergraduate students, followed by qualitative analysis of questionnaire data in order to look for indications of participants experiencing broadened thinking with respect to the function concept. The theoretical evaluation confirmed the IFI to be sound and providing opportunities for addressing common conceptual difficulties of the function concept. The qualitative analysis provided evidence of the participants’ expanded concept images. It was concluded that the designed intervention, the IFI, is sound and viable and shows promise with respect to increased understanding of the function concept.

Keywords

• function concept
• image functions
• apos theory
• genetic decomposition
• mathematics